Hardy-Littlewood inequality and Lp-Lq Fourier multipliers on compact hypergroups Ghent University
This paper deals with the inequalities comparing the norm of a function on a compact hypergroup and the norm of its Fourier coefficients. We prove the classical Paley inequality in the setting of compact hypergroups which further gives the Hardy-Littlewood and Hausdorff-Young-Paley inequalities in the noncommutative context. We establish Hormander's L-p- L-q Fourier multiplier theorem on compact hypergroups for 1 < p <= 2 <= q < ...